Blinded Commitment

In a blinded commitment scheme, a user first creates a standard cryptographic commitment (e.g., using a hash function like SHA-256) to a secret value. This commitment is then blinded by combining it with a random secret, often through multiplication with a blinding factor in a cryptographic group. The resulting blinded output is sent to a verifier or service. The core property is unlinkability: the verifier cannot correlate the blinded commitment with the user's original, unblinded commitment or identity, even if the secret value is later revealed.

This technique is fundamental to privacy-preserving protocols. A canonical example is in blind signature schemes, where a user can obtain a signature on a message (like a token or coin) without the signer learning the message's content. The user blinds the message, the signer signs the blinded data, and the user then unblinds the signature to obtain a valid signature on the original message. This prevents the signer from later tracing the signed token back to the specific issuance transaction, enabling systems like digital cash.

In blockchain contexts, blinded commitments are crucial for anonymous credentials and privacy-focused transactions. They allow a prover to demonstrate they possess a valid credential (e.g., proof of age or membership) or a valid unspent transaction output (UTXO) without revealing which specific credential or UTXO it is. This is achieved through complex zero-knowledge protocols where the commitment serves as a hidden input. The blinding ensures that even repeated interactions with the same verifier cannot be linked together, enhancing user privacy.

The security of a blinded commitment relies on the properties of the underlying cryptographic group (often elliptic curve groups) and the assumption that certain computational problems, like the discrete logarithm problem, are hard. If an attacker could reverse the blinding process, the unlinkability property would fail. Proper implementation requires high-quality randomness for the blinding factor; predictable or reused blinding factors can compromise the entire system's privacy guarantees.

A blinded commitment is a two-stage protocol combining a commitment scheme and a blind signature scheme. First, a user creates a cryptographic commitment to a secret value (like a vote or a bid). This commitment is then blinded using a random factor, obscuring the original data. The user sends this blinded commitment to an authority (e.g., a voting server or an auction house). The authority, unable to see the underlying value, applies its digital signature to the blinded data and returns it.

The user then unblinds the received signature. This process removes the random blinding factor, resulting in a valid signature from the authority on the original, unblinded commitment. Crucially, the authority cannot link this final, signed commitment back to the initial blinded request it processed. This provides unlinkability, a core property separating blinded commitments from simple commitments.

The final, signed commitment can now be presented to a third party (like a blockchain smart contract) to prove the authority approved the committed value, without revealing the user's identity to the authority. Common implementations use cryptographic building blocks like Pedersen Commitments for the commitment and the RSA blind signature scheme or blind Schnorr signatures for the blinding operation.

This mechanism is foundational for privacy-preserving systems. Key use cases include anonymous voting (where a voter gets a ballot authorized without being identified), anonymous credentials, and privacy-focused auctions. It ensures that the authorizing party provides a service (issuing a signature) based on policy, not on the specific content or originator of the request, thereby preventing censorship or discrimination based on the committed data.

In a blockchain context, a user might generate a blinded commitment to a transaction detail off-chain, have it signed by a service, and then submit the unblinded, signed proof on-chain. This allows the network to verify the authorization without the signing service learning which on-chain action corresponds to which user's request, enhancing transactional privacy.

A blinded commitment flow is a cryptographic protocol that allows a prover to commit to a secret value, such as a balance or identity, without revealing it to a verifier. The process begins with the prover generating a cryptographic commitment, which is a one-way function output that binds the secret. Crucially, this commitment is then blinded using a random value, creating a zero-knowledge proof that the committed data satisfies certain conditions—like being within a valid range—while the actual data remains hidden. This initial step ensures both binding (the prover cannot change the secret later) and hiding (the verifier learns nothing about the secret).

The flow typically involves the verifier sending a challenge to the prover after receiving the blinded commitment. The prover then constructs a response, often called a proof, that is cryptographically linked to both the secret and the random blinding factor. By verifying this proof against the original commitment, the verifier can be statistically convinced of the statement's truth—for example, that a transaction input does not exceed a certain amount—without learning the underlying data. This challenge-response mechanism is fundamental to zero-knowledge proofs and bulletproofs used in confidential transactions.

In practical blockchain applications, such as confidential assets or privacy-preserving identity systems, this flow enables selective disclosure. A user can prove they have sufficient funds for a transaction or the right credentials for access, all while keeping the exact amounts and identifiers private. The entire sequence—commit, blind, challenge, respond, verify—forms a secure, trust-minimized interaction that is visualized as a clear data pipeline between parties, highlighting where information is hidden, transformed, and validated.

A blinded commitment is a two-step cryptographic protocol that combines a commitment scheme with a blind signature. First, a user creates a cryptographic commitment to a secret value (like a transaction amount or a vote). This commitment is then 'blinded' using a random factor before being sent to an authority (e.g., a central bank in a digital currency system or a coordinator in a voting protocol). The authority signs this blinded commitment without seeing the underlying data, and the user can later 'unblind' the signature to obtain a valid, authorized commitment that is cryptographically unlinkable to the original request.

The core security properties are hiding, binding, and unlinkability. The commitment itself keeps the value secret (hiding) and prevents the user from changing it later (binding). The blinding process ensures the authorizing entity cannot correlate the signed, final commitment with the initial blinded request it processed. This is crucial for privacy in systems like Chaumian e-cash and certain blockchain transaction designs, where a central issuer must authorize tokens without being able to track their subsequent circulation.

In implementation, a common construction uses a Pedersen Commitment for the commitment scheme and the blind signature algorithm based on the RSA or Schnorr signature schemes. For example, the value v is committed as C = g^v * h^r, where r is a random blinding factor and g, h are public generator points. This commitment C is then multiplied by a blinding factor b before being sent for signing. After receiving the blind signature, the user divides it by b to derive a signature on the original C.

A key application is in confidential transactions and privacy-preserving protocols. In Mimblewimble and similar blockchains, blinded commitments (often called Pedersen Commitments) represent encrypted amounts, allowing the network to verify that no money is created out of thin air—by checking that the sum of input commitments equals the sum of output commitments—without revealing the actual values. This provides strong financial privacy while maintaining public auditability.

The technique must be carefully designed to avoid vulnerabilities. If the blinding process is not cryptographically sound, it can lead to linkability attacks, breaking privacy. Furthermore, the security of the entire system depends on the underlying assumptions of the discrete logarithm problem (for Pedersen Commitments) and the signature scheme's resistance to forgery. Proper implementation requires secure random number generation for the blinding factors to prevent correlation.